The Evolved Motions of a Marine Riser or Pipeline

Analytical, experimental and computational models have historically been heavily simplified, linearized, and otherwise reduced. This paper shows how such model reductions eliminate the fundamental geometric changes that determine real behavior in cables, strings, moorings, guys, pipelines, riser, plates, skins, subsea hulls, and other such slender and thin structures. The paper details each physical quantity that we must add back into our overly reduced models to improve the basic nature, evolution, and accuracy of the resulting motions and vibrations. For example, even slight changes in local rotation anywhere along a cable can create large nonlinear changes in the dynamic nature of its behavior. The evolved complexity of the resulting global motions and vibrations in space and time often defy what we normally expect from such a simple structure. Although this paper focuses on the modeling of deep-water moorings and risers of an ocean platform, the same geometric effect is fundamental to most science and engineering models. Understanding how small changes in geometry can nonlinearly affect any structured behavior will help demystify much of the poorly-understood motions and vibrations in a large diversity of applications, including induced vibrations, sound, structural acoustics, aero-elasticity, sound, light and atomic radiation.

A Multidomain Spectral Method for Analysis of Interior Vibroacoustic Systems with Segmented Boundaries

Spectral methods have previously been applied to analyze a multitude of vibration and acoustic problems due to their high computational efficiency. However, their application to interior structural acoustics systems has been limited to the analysis of a single plate coupled to a fluid-filled cavity. In this work, a general multidomain spectral approach is proposed for the eigenvalue and steady-state vibroacoustic analyses of interior structural-acoustic problems with discontinuous boundaries. The unified formulation is derived by means of a generalized variational principle in conjunction with the spectral discretization procedure. The established framework enables one to easily accommodate complex systems consisting of both a structure assembly and a built-up cavity with moderate geometric complexities and to effectively analyze vibroacoustic behaviors with sufficient accuracy at relatively high frequencies. Two practical examples are chosen to demonstrate the flexibility and efficiency of the proposed formulation: a built-up cavity backed by an assembly of multiple connected plates with arbitrary orientations and a thick irregular elastic solid coupled with a heavy acoustic medium. Comparison to finite element simulations and convergence studies for these two examples illustrate the considerable computational advantage of the method as compared to finite element procedures.

Partitioned Coupling for Structural Acoustics

We expand the second-order fluid–structure coupling scheme of Farhat et al. (1998, “Load and Motion Transfer Algorithms for 19 Fluid/Structure Interaction Problems With Non-Matching Discrete Interfaces: Momentum and Energy Conservation, Optimal Discretization and Application to Aeroelasticity,” Comput. Methods Appl. Mech. Eng., 157(1–2), pp. 95–114; 2006, “Provably Second-Order Time-Accurate Loosely-Coupled Solution Algorithms for Transient Nonlinear Computational Aeroelasticity,” Comput. Methods Appl. Mech. Eng., 195(17), pp. 1973–2001) to structural acoustics. The staggered structural acoustics solution method is demonstrated to be second-order accurate in time, and numerical results are compared to a monolithically coupled system. The partitioned coupling method is implemented in the Sierra Mechanics software suite, allowing for the loose coupling of time domain acoustics in sierra/sd to structural dynamics (sierra/sd) or solid mechanics (sierra/sm). The coupling is demonstrated to work for nonconforming meshes. Results are verified for a one-dimensional piston, and the staggered and monolithic results are compared to an exact solution. Huang, H. (1969, “Transient Interaction of Plane Acoustic Waves With a Spherical Elastic Shell,” J. Acoust. Soc. Am., 45(3), pp. 661–670) sphere scattering problem with a spherically spreading acoustic load demonstrates parallel capability on a complex problem. Our numerical results compare well for a bronze plate submerged in water and sinusoidally excited (Fahnline and Shepherd, 2017, “Transient Finite Element/Equivalent Sources Using Direct Coupling and Treating the Acoustic Coupling Matrix as Sparse,” J. Acoust. Soc. Am., 142(2), pp. 1011–1024).